Products of residue currents of Cauchy–Fantappiè–Leray type

With a given holomorphic section of a Hermitian vector bundle, one can associate a residue current by means of Cauchy–Fantappiè–Leray type formulas. In this paper we define products of such residue currents. We prove that, in the case of a complete intersection, the product of the residue currents of a tuple of sections coincides with the residue current of the direct sum of the sections.     

An Implicit Iteration Process with Errors for a Finite Family of r-strictly Asymptotically Pseudocontractive Mappings

In this paper,we will establish several strong convergence theorems for the approximation ofcommon fixed points of r-strictly asymptotically pseudocontractive mappings in uniformly convex Banachspaces using the modiied implicit iteration sequence with errors,and prove the necessary and sufficient conditionsfor the convergence of the sequence.Our results generalize,extend and improve the recent work,in thistopic.     

A Penrose-like inequality for maximal asymptotically flat spin initial data sets

We prove a Penrose-like inequality for the mass of a large class of constant mean curvature (CMC) asymptotically flat n-dimensional spin manifolds which satisfy the dominant energy condition and have a future converging, or past converging compact and connected boundary of non-positive mean curvature and of positive Yamabe invariant. We prove that for every n ≥ 3 the mass is bounded from below by an expression involving the norm of the linear momentum, the volume of the boundary, dimensionless geometric constants and some normalized Sobolev ratio.     

Dynamic programming in cricket: optimizing batting order for a sticky wicket

In cricket, a rain-affected pitch can make batting more difficult than normal. Several other conditions such as poor light or an initially lively pitch, may also result in difficulties for the batsmen. In this note, we refer to all of them as ‘sticky wickets’. On sticky wickets, lower order batsmen are often sent into ‘hold the fort’ until conditions improve. In this paper, a stochastic dynamic programming model is used to examine the appropriateness of this policy. The model suggests that the tactic is often optimal when the sticky wicket persists until the end of the day's play, but not often when the sticky wicket is transitory. In some circumstances, it is worthwhile, on a normal wicket near the end of the day, to send in a lower order batsman to hold the fort (a night watchman): when the wicket is sticky, this tactic is even more worthwhile.     

Characteristics of transmission of electrons in a quantum wire tangentially attached to a superconductor ring threaded by magnetic flux

We present numerical investigations of the transmission properties of electrons in a normal quantum wire tangentially attached to a superconductor ring threaded by magnetic flux. A point scatterer with a δ -function potential is placed at node to model scattering effect. We find that the transmission characteristics of electrons in this structure strongly depend on the normal or superconducting state of the ring. The transmission probability as a function of the energy of incident electrons, in the case of a superconductor ring threaded by one quantum magnetic flux, emerges one deep dip, imposed upon the first broad bump in spectrum. This intrinsic conductance dip originates from the superconductor state of the ring. When increasing the magnetic flux from one quantum magnetic flux to two, the spectrum shifts toward higher energy region in the whole. This conductance dip accordingly shifts and appears in the second bump. In the presence of a point-scatterer at the node, the spectrum is substantially modified. Based on the condition of the formation of the standing wave functions in the ring and the broken of the time-reserve symmetry of Schr?dinger equation after switching magnetic flux, the characteristics of transmission of electrons in this structure can be well understood. Received 6 November 2001     

Controlling global stochasticity of Hamiltonian systems by nonlinear perturbation

A method of controlling global stochasticity in Hamiltonian systems by applying nonlinear perturbation is proposed. With the well-known standard map we demonstrate that this control method can convert global stochasticity into regular motion in a wide chaotic region for arbitrary initial condition, in which the control signal remains very weak after a few kicks. The system in which chaos has been controlled approximates to the original Hamiltonian system, and this approach appears robust against small external noise. The mechanism underlying this high control efficiency is intuitively explained. Received 15 January 2002 Published online 6 June 2002     

Development of a “Built-in” Scanning Near Field Microscope Head for an Atomic Force Microscope System and Stress Mapping of an Al2O3/ZrO2 Eutectic Composite

We constructed a scanning near-field optical microscope (SNOM) on a commercially available atomic force microscopy (AFM) apparatus (SPM-9500J2; Shimadzu Corp.) to measure the stress distribution in ceramic composite materials. Features of our SNOM system are: (1) a compact SNOM head substituted for the original AFM head; (2) a wide scanning range (125 × 125 μm²) inherited from the original scanner; (3) use of conventional shear-force regulation; (4) an optical system for the illumination-collection (I-C) mode; (5) excitation by a 488 nm line of an Ar-ion laser, and (6) light detection by photon counting or a polychromator equipped with an electronically cooled charge coupled device (CCD). This SNOM system was used to measure the surface structure and stress distribution of an Al₂O₃/ZrO₂ eutectic composite. We simultaneously measured topographic images and fluorescence spectra of an Al₂O₃/ZrO₂ eutectic composite. We estimated its peak intensity, peak position, and peak width from the fluorescence spectrum during scanning, which respectively correspond to the abundance of Al₂O₃, stress in the grain, and the anisotropy of that stress. Mapping images showed that the stress and its anisotropy were weaker in the center of the Al₂O₃ grain than its boundary between Al₂O₃ and ZrO₂. That observation suggests that Al₂O₃ underwent intense anisotropic stress induced by volume expansion in the phase transition of ZrO₂ from the cubic phase to the monoclinic phase during preparation.